DRAFT IEEE Standard for Binary Floating-Point Arithmetic - Sonic.net

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DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20 to the precision and exponent range of a narrower format, even if that rounded value is stored in a wider format. §6 [FOOTNOTE: If it is only possible to round to narrower precision with a wider exponent range, it can be unnecessarily complicated to exactly emulate the behavior of systems that only support narrower precisions single or double. In particular, emulating the overflow and underflow behavior can be costly.] §6 Note that to meet the specifications in 4.1, the result cannot suffer more than one rounding error. §6 [Should this rounding precision section be outlawed for decimal? -JDD] Copyright © 2003 by the Institute of Electrical and Electronics Engineers, Inc. This document is an unapproved draft of a proposed IEEE-SA Standard - USE AT YOUR OWN RISK. See statement on page 1. Page 38
DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20 5. Operations All conforming implementations of this standard shall provide operations to add, subtract, multiply, divide, compute fused multiply-add §FMA, extract the square root, find the remainder, round to integer in floating-point format, convert between different floating-point formats, convert between floating-point and integer formats, convert binary decimal, and compare, and conversion between internal floating-point formats and external decimal formats. Whether copying without change of format is considered an operation is an implementation option.§BI Except for conversion between internal floating-point formats and external decimal formats binary decimal conversion, each of the operations shall be performed as if it first produced an intermediate result correct to infinite precision and with unbounded range, and then coerced this intermediate result to fit in the destination's format (see Sections 4 and 7). Section 6 augments the following specifications to cover ±0, ±¥, and NaN; Section 7 enumerates exceptions caused by exceptional operands and exceptional results. In this standard, some operators such as fused multiply-add fma(a,b,c) and predicates such as isnormal(x) are written as named generic functions due to lack of widely-accepted operator notations; in a specific programming environment they might be represented by operators, or by families of format-specific functions, or by generic functions whose names may differ from those in this standard. §FMA [To mesh better with the claim in Section 4 that “rounding modes affect all arithmetic operations,” arithmetic operations should be more clearly defined as a set. From reading section 4, one could conclude that comparison is an arithmetic operation. Section 4 of 854 states “The rounding modes affect all arithmetic operations except comparison and remainder.” -JDD] 5.1. Arithmetic For each supported format §FMA, an implementation shall provide the add, subtract, multiply, divide, and remainder operations for any two operands of the same format, and a fused multiply-add operation for any three operands of the same format §FMA; for each supported format; it should also provide these operations for operands of differing formats. The destination format (regardless of Copyright © 2003 by the Institute of Electrical and Electronics Engineers, Inc. This document is an unapproved draft of a proposed IEEE-SA Standard - USE AT YOUR OWN RISK. See statement on page 1. Page 39
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DRAFT IEEE Standard for Binary Floating-Point Arithmetic - Sonic.net

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